A law which is not yet in effect does require landlords to permit service dogs. See link below. A current law which may apply, the Human Rights, Citizenship and Multiculturalism Act, does prohibit discrimination based on a person's disability. See the section that discusses tenancy below. Check with a local attorney to learn how this applies in your own situation.
= Human Rights, Citizenship and Multiculturalism Act =
Discrimination re tenancy 5 No person shall (a) deny to any person or class of persons the right to occupy as a tenant any commercial unit or self‑contained dwelling unit that is advertised or otherwise in any way represented as being available for occupancy by a tenant, or (b) discriminate against any person or class of persons with respect to any term or condition of the tenancy of any commercial unit or self‑contained dwelling unit, because of the race, religious beliefs, colour, gender, physical disability, mental disability, ancestry, place of origin, marital status, source of income or family status of that person or class of persons or of any other person or class of persons. RSA 1980 cI‑2 s4;1985 c33 s2;1990 c23 ss2,3;1996 c25 s6